Final answer:
The length of PQ in a quadrilateral with equal side lengths in coordinate geometry can be calculated using the distance formula, which is the same for all sides of the quadrilateral, making a. |P - Q| the correct answer.
Step-by-step explanation:
If all sides of a quadrilateral PQRS are equal in coordinate geometry, then the length of the side PQ can be found using the distance formula, which is derived from the Pythagorean theorem.
The distance PQ can be represented as |PQ|, which is equivalent to the length of any other side of the quadrilateral due to its property of having equal length sides. So the length of PQ would be equivalent to |RS|, |SP|, or |QR|, since all sides are equal in length.
To find PQ, you would subtract the coordinates of P from the coordinates of Q (or vice versa) and apply the Pythagorean theorem, calculating the distance as the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of points P and Q.
Therefore, the correct answer to the question is: a. |P - Q|.